Total least-squares iterative closest point algorithm based on lie algebra

Abstract

In geodetic surveying, input data from two coordinates are needed to compute rigid transformations. A common solution is a least-squares algorithm based on a Gauss-Markov model, called iterative closest point (ICP). However, the error in the ICP algorithm only exists in target coordinates, and the algorithm does not consider the source model's error. A total least-squares (TLS) algorithm based on an errors-in-variables (EIV) model is proposed to solve this problem. Previous total least-squares ICP algorithms used a Euler angle parameterization method, which is easily affected by a gimbal lock problem. Lie algebra is more suitable than the Euler angle for interpolation during an iterative optimization process. In this paper, Lie algebra is used to parameterize the rotation matrix, and we re-derive the TLS algorithm based on a GHM (Gauss-Helmert model) using Lie algebra. We present two TLS-ICP models based on Lie algebra. Our method is more robust than previous TLS algorithms, and it suits all kinds of transformation matrices.